Hooray! So. Slave from snowy land who can run and jump and fight super sfx-fast helps his owner defeat bad guys using bull stampede. Master dies, but soon gets new master as Red Armor dude being chased by darkwing snowland fella. Slave rescues Queen, kills king, Red Armor is blamed. Queen once sold her happiness to mythic swamp lady for beauty + wealth (after betraying kid who will grow up to be fey supervillain). Slave rescues her a few more times, sometimes fighting and sometimes joined by Red Armor or Darkwing. Showdown with Fey leaves Slave wearing immortal darkwing suit, Queen freed of her curse, everyone else dead.
Maybe the “promise” of the title is the Queen’s. She is forced to keep that one by the goddess, while everyone else breaks their promises (of love, slavery, kinship, etc). Pretty excellent looking movie, and satisfactory ending (more so than Zhang Yimou’s last three pictures?).